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The mean of $5$ numbers is $4$ . If $1$ is added to each number, then the new mean is

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4

5

3

5.5

answer is B.

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Detailed Solution

It is given that the mean of

5

numbers is

4

.
We have to find the new mean when

1

is added to each number.
Let the five numbers be

a, b, c, d, e

.
We know that,

Mean = \frac{Sum of observations}{Number of observ a tions}

\Rightarrow 4 = \frac{a + b + c + d + e}{5}

\Rightarrow 4 \times 5 = a + b + c + d + e

\Rightarrow 20 = a + b + c + d + e

— (1)
If

1

is added to each number,

Sum of observations = (a + 1) + (b + 1) + (c + 1) + (d + 1) + (e + 1)

\Rightarrow Sum of observations = 5 + a + b + c + d + e

Substituting eq(1) in above equation,

\Rightarrow Sum of observations = 5 + 20

\Rightarrow Sum of obse r vations = 25

Therefore,

Mean = \frac{Sum of observations}{Number of observations}

\Rightarrow New mean = \frac{25}{5}

\Rightarrow New mean = 5

Therefore, the new mean is

5

.
Hence, the correct option is 2.

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